264 research outputs found
Scalable k-Means Clustering via Lightweight Coresets
Coresets are compact representations of data sets such that models trained on
a coreset are provably competitive with models trained on the full data set. As
such, they have been successfully used to scale up clustering models to massive
data sets. While existing approaches generally only allow for multiplicative
approximation errors, we propose a novel notion of lightweight coresets that
allows for both multiplicative and additive errors. We provide a single
algorithm to construct lightweight coresets for k-means clustering as well as
soft and hard Bregman clustering. The algorithm is substantially faster than
existing constructions, embarrassingly parallel, and the resulting coresets are
smaller. We further show that the proposed approach naturally generalizes to
statistical k-means clustering and that, compared to existing results, it can
be used to compute smaller summaries for empirical risk minimization. In
extensive experiments, we demonstrate that the proposed algorithm outperforms
existing data summarization strategies in practice.Comment: To appear in the 24th ACM SIGKDD International Conference on
Knowledge Discovery & Data Mining (KDD
Clustering for binary data sets by using genetic algorithm-incremental K-means
This research was initially driven by the lack of clustering algorithms that specifically focus in binary data. To overcome this gap in knowledge, a promising technique for analysing this type of data became the main subject in this research, namely Genetic Algorithms (GA). For the purpose of this research, GA was combined with the Incremental Kmeans (IKM) algorithm to cluster the binary data streams. In GAIKM, the objective function was based on a few sufficient statistics that may be easily and quickly calculated on binary numbers. The implementation of IKM will give an advantage in terms of fast convergence. The results show that GAIKM is an efficient and effective new clustering algorithm compared to the clustering algorithms and to the IKM itself. In conclusion, the GAIKM outperformed other clustering algorithms such as GCUK, IKM, Scalable K-means (SKM) and K-means clustering and paves the way for future research involving missing data and outliers
Parametric t-Distributed Stochastic Exemplar-centered Embedding
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been
widely adopted for data visualization and out-of-sample data embedding without
further computationally expensive optimization or approximation. However, the
performance of pt-SNE is highly sensitive to the hyper-parameter batch size due
to conflicting optimization goals, and often produces dramatically different
embeddings with different choices of user-defined perplexities. To effectively
solve these issues, we present parametric t-distributed stochastic
exemplar-centered embedding methods. Our strategy learns embedding parameters
by comparing given data only with precomputed exemplars, resulting in a cost
function with linear computational and memory complexity, which is further
reduced by noise contrastive samples. Moreover, we propose a shallow embedding
network with high-order feature interactions for data visualization, which is
much easier to tune but produces comparable performance in contrast to a deep
neural network employed by pt-SNE. We empirically demonstrate, using several
benchmark datasets, that our proposed methods significantly outperform pt-SNE
in terms of robustness, visual effects, and quantitative evaluations.Comment: fixed typo
Fast k-means based on KNN Graph
In the era of big data, k-means clustering has been widely adopted as a basic
processing tool in various contexts. However, its computational cost could be
prohibitively high as the data size and the cluster number are large. It is
well known that the processing bottleneck of k-means lies in the operation of
seeking closest centroid in each iteration. In this paper, a novel solution
towards the scalability issue of k-means is presented. In the proposal, k-means
is supported by an approximate k-nearest neighbors graph. In the k-means
iteration, each data sample is only compared to clusters that its nearest
neighbors reside. Since the number of nearest neighbors we consider is much
less than k, the processing cost in this step becomes minor and irrelevant to
k. The processing bottleneck is therefore overcome. The most interesting thing
is that k-nearest neighbor graph is constructed by iteratively calling the fast
-means itself. Comparing with existing fast k-means variants, the proposed
algorithm achieves hundreds to thousands times speed-up while maintaining high
clustering quality. As it is tested on 10 million 512-dimensional data, it
takes only 5.2 hours to produce 1 million clusters. In contrast, to fulfill the
same scale of clustering, it would take 3 years for traditional k-means
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